I'm really not sure where either go, as neither of them seem to be a standard Grignard reagent reaction. The first is missing an Mg between the carbon group and the halogen, and the second is missing both a carbonyl (C=O) and acidic conditions. Are there alternatives to the standard reaction?

There's no way for any of us to answer this question. We don't know how the question was worded or if you were assigned to find flaws.

In the first case you are missing a magnesium as you've indicated. In the second case you are given a primary alkyne as a reagent. Review your list of suitable/unsuitable reagents for this type of reaction for your answer.